Final answer:
Atlanta is the only U.S. state capital that has hosted a summer Olympic Games, specifically in 1996. Option 1 is correct.
Step-by-step explanation:
Among the U.S. state capitals, Atlanta stands as the singular host of a summer Olympic Games, notably welcoming the world during the Centennial Olympic Games in 1996. This momentous event etched a significant chapter in Atlanta, Georgia's history, serving as a grand international assembly that captured global attention and participation.
Contrastingly, Los Angeles, California, although a two-time host of the Olympic Games in 1932 and 1984, is not a state capital. Despite its substantial Olympic legacy, the city does not carry the distinction of being a political capital within its state. Salt Lake City, on the other hand, earned acclaim as a host of the Winter Olympics but has not been the venue for the Summer Olympics. As for Denver, it has yet to witness the honor of hosting any Olympics, making it an untouched frontier in the realm of Olympic competitions.
Atlanta's role as a state capital that also hosted the Summer Olympics underlines the unique convergence of political and sporting significance, amplifying the city's global profile and contributing to the diverse Olympic landscape across various American cities.